You have two lengths of rope that take exactly 60 minutes to burn. The ropes burn unevenly so if you cut the rope in half, burning a half will not necessarily take 30 minutes.
How do you precisely measure 45 minutes using these two ropes?
Light one end of one rope and both ends of the other rope at the same time. Even though the rope is uneven, burning it from both ends will take 30 minutes to burn (it just won’t meet exactly in the middle).
After the rope that was lit on both ends is done, the other rope will have been burning for 30 minutes, so there will be 30 minutes left on it. At this point, you immediately light the remaining end of that rope. This rope will then burn for 15 more minutes, for a total of 45 minutes.
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